发表机构
Maastricht University（马斯特里赫特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对含固定效应的模型提出面板信息矩阵（PIM）检验，解决了信息矩阵检验的规模偏差、混淆异质性与误设等问题，模拟验证了其在中等长度面板中的有效性。
AI 中文摘要
信息矩阵（IM）检验是基于似然模型的自然设定检验，但横截面实施的检验通常规模偏差严重，会混淆被忽略的异质性与分布误设，且需要三阶导数。我们针对含固定效应的模型提出面板信息矩阵（PIM）检验，显式固定效应可将函数形式误设与时不变未观测异质性分离。虽然轮廓最大似然估计量继承了阶为O(1/T)的 incidental 参数偏差，但轮廓PIM的主导偏差阶为√n/T，因此当n/T²→0时渐近可忽略，包括矩形情形n/T→常数，且在抛物线渐近n/T²→ρ∈(0,∞)时稳定。该稳健性源于指标以√n而非√(nT)的速率波动，相同速率论证使三阶导数校正渐近不必要，故检验仅使用一阶和二阶似然导数。模拟结果证实，即使θ的Wald检验规模偏差严重，渐近PIM临界值在中等长度面板中已足够，而当ρ>0时，参数自助法可大幅消除规模扭曲。
英文摘要
The Information Matrix (IM) test is a natural specification check for likelihood-based models, yet cross-sectional implementations are often badly sized, confound neglected heterogeneity with distributional misspecification, and require third derivatives. We develop the panel information matrix (PIM) test for models with fixed effects. Explicit fixed effects isolate functional-form misspecification from time-invariant unobserved heterogeneity. Although the profile maximum likelihood estimator inherits incidental-parameter bias of order $O(1/T)$, the leading bias of the profile PIM is of order $\sqrt{n}/T$, so it is asymptotically negligible whenever $n/T^2\to 0$, which includes the rectangular regime $n/T\to\mathrm{const}$, and stabilizes under parabolic asymptotics $n/T^2\toρ\in(0,\infty)$. This robustness arises because the indicator fluctuates at rate $\sqrt{n}$ rather than $\sqrt{nT}$. The same rate argument makes third-derivative corrections asymptotically unnecessary, so the test uses only first- and second-order likelihood derivatives. Simulations confirm that asymptotic PIM critical values suffice in moderately long panels, even when Wald tests for $θ$ are badly sized, while a parametric bootstrap largely removes size distortions when $ρ>0$.
